Primordial Black Holes and Cosmological Phase Transitions Report ...

PBHs and Cosmological Phase Transitions 49
Figure 11: Mass spectrum of supersymmetric particles and the Higgs boson
according to the SPS1a scenario (cf. Table 11 for mass values). Here ( ˜ lL, ˜ lR, ˜νl)
and (˜qL, ˜qR) represent the first and the second families of sleptons and squarks
respectively (e.g. Aguilar–Saavedra et al., 2006; Allanach et al., 2002).
is the energy (E = p 2 + m 2 ) and the sign is + for fermions and − for bosons.
The quantity µ = µ(T ) is the chemical potential 23 of the species. The chemical
potential is conserved in every collision (e.g. Lyth, 1993).
In the early Universe all known particle species are freely created and destroyed.
The only significant restriction is that each collision must respect conservation
of the electric charge, baryon number and the three lepton numbers.
Since the photon carries none of these charges it turns out that µγ = 0 and
equation (95) leads to the blackbody distribution (e.g. Lyth 1993). The same
goes for any particle which is its own antiparticle. If the antiparticle is distinct,
23 In the context of Particle Physics the chemical potential measures the tendency of particles
to diffuse. Particles tend to diffuse from regions of high chemical potential to those of low
chemical potential. In a system with many particle species each of them has its own chemical
potential. The chemical potential of the i-th particle species is defined as
µi = ∂U
∂Ni s,V,N j=i
where U is the total internal energy of the system, s is the entropy, V is the volume and
Ni is the number of particles of the i-th species. Being a function of internal energy, the
chemical potential applies equally to both fermion and boson particles. That is, in theory,
any fundamental particle can be assigned a value of chemical potential, depending upon how
it changes the internal energy of the system into which it is introduced. QCD matter is a
prime example of a system in which many such chemical potentials appear (e.g. Baierlein,
2001).